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| start [2019/10/11 11:29] – alexanderg | start [2019/12/12 08:11] – alexanderg | ||
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| - | < | + | ===== Structure of the documentation ===== |
| - | < | + | |
| - | <meta http-equiv=Content-Type content=" | + | The documentation is structured |
| - | <meta name=ProgId content=Word.Document> | + | |
| - | <meta name=Generator content=" | + | |
| - | <meta name=Originator content=" | + | |
| - | <link rel=File-List href=" | + | |
| - | <link rel=Edit-Time-Data | + | |
| - | href=" | + | |
| - | <link rel=OLE-Object-Data | + | |
| - | href=" | + | |
| - | <!--[if !mso]> | + | |
| - | < | + | |
| - | v\:* {behavior: | + | |
| - | o\:* {behavior: | + | |
| - | w\:* {behavior: | + | |
| - | .shape {behavior: | + | |
| - | </ | + | |
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| - | <link rel=dataStoreItem | + | |
| - | href=" | + | |
| - | target=" | + | |
| - | <link rel=themeData | + | |
| - | href=" | + | |
| - | <link rel=colorSchemeMapping | + | |
| - | href=" | + | |
| - | <!--[if gte mso 9]>< | + | |
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| - | DefSemiHidden=" | + | |
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| - | < | + | |
| - | <!-- | + | |
| - | /* Font Definitions */ | + | |
| - | | + | |
| - | {font-family: | + | |
| - | panose-1:5 0 0 0 0 0 0 0 0 0; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family:" | + | |
| - | panose-1:2 4 5 3 5 4 6 3 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family: | + | |
| - | panose-1:2 15 5 2 2 2 4 3 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family: | + | |
| - | panose-1:2 11 6 4 3 5 4 4 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | @font-face | + | |
| - | {font-family: | + | |
| - | panose-1:2 4 5 3 5 4 6 3 2 4; | + | |
| - | mso-font-charset: | + | |
| - | mso-generic-font-family: | + | |
| - | mso-font-pitch: | + | |
| - | mso-font-signature: | + | |
| - | /* Style Definitions */ | + | |
| - | | + | |
| - | {mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-parent:""; | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | h1 | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | page-break-after: | + | |
| - | mso-outline-level: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-themeshade: | + | |
| - | mso-font-kerning: | + | |
| - | mso-fareast-language: | + | |
| - | h2 | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | page-break-after: | + | |
| - | mso-outline-level: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-fareast-language: | + | |
| - | h3 | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | page-break-after: | + | |
| - | mso-outline-level: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoFootnoteText, | + | |
| - | {mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-link:" | + | |
| - | margin: | + | |
| - | margin-bottom: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoCaption, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-fareast-language: | + | |
| - | font-weight: | + | |
| - | span.MsoFootnoteReference | + | |
| - | {mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | vertical-align: | + | |
| - | p.MsoAcetate, | + | |
| - | {mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-link:" | + | |
| - | margin: | + | |
| - | margin-bottom: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraph, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraphCxSpFirst, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-type: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraphCxSpMiddle, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-type: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | margin-bottom: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | p.MsoListParagraphCxSpLast, | + | |
| - | {mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-qformat: | + | |
| - | mso-style-type: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | mso-add-space: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | span.berschrift1Zchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link:" | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | mso-themeshade: | + | |
| - | font-weight: | + | |
| - | span.MTEquationSection | + | |
| - | {mso-style-name: | + | |
| - | mso-style-unhide: | + | |
| - | color: | + | |
| - | display: | + | |
| - | mso-hide: | + | |
| - | mso-ansi-language: | + | |
| - | p.MTDisplayEquation, | + | |
| - | {mso-style-name: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-link:" | + | |
| - | mso-style-next: | + | |
| - | margin-top: | + | |
| - | margin-right: | + | |
| - | margin-bottom: | + | |
| - | margin-left: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | tab-stops: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-ansi-language: | + | |
| - | mso-fareast-language: | + | |
| - | span.MTDisplayEquationZchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link: | + | |
| - | mso-ansi-language: | + | |
| - | span.berschrift2Zchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link:" | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | font-weight: | + | |
| - | span.berschrift3Zchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link:" | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family:" | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | color:# | + | |
| - | mso-themecolor: | + | |
| - | font-weight: | + | |
| - | span.FunotentextZchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link: | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | span.SprechblasentextZchn | + | |
| - | {mso-style-name:" | + | |
| - | mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | mso-style-locked: | + | |
| - | mso-style-link: | + | |
| - | mso-ansi-font-size: | + | |
| - | mso-bidi-font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-bidi-font-family: | + | |
| - | span.SpellE | + | |
| - | {mso-style-name:""; | + | |
| - | mso-spl-e: | + | |
| - | span.GramE | + | |
| - | {mso-style-name:""; | + | |
| - | mso-gram-e: | + | |
| - | .MsoChpDefault | + | |
| - | {mso-style-type: | + | |
| - | mso-default-props: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | .MsoPapDefault | + | |
| - | {mso-style-type: | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | /* Page Definitions */ | + | |
| - | | + | |
| - | {mso-footnote-separator: | + | |
| - | mso-footnote-continuation-separator: | + | |
| - | mso-endnote-separator: | + | |
| - | mso-endnote-continuation-separator: | + | |
| - | @page WordSection1 | + | |
| - | {size: | + | |
| - | margin: | + | |
| - | mso-header-margin: | + | |
| - | mso-footer-margin: | + | |
| - | mso-paper-source: | + | |
| - | div.WordSection1 | + | |
| - | {page: | + | |
| - | /* List Definitions */ | + | |
| - | @list l0 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l0:level1 | + | |
| - | {mso-level-start-at: | + | |
| - | mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | @list l0:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l0:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level4 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l0:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level7 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l0:level8 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l0:level9 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l1:level1 | + | |
| - | {mso-level-start-at: | + | |
| - | mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | @list l1:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l1:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level4 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l1:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level7 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l1:level8 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l1:level9 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l2 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l2:level1 | + | |
| - | {mso-level-start-at: | + | |
| - | mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | @list l2:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l2:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l2:level4 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l2:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l2:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l2:level7 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l2:level8 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l2:level9 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l3 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l3:level1 | + | |
| - | {mso-level-start-at: | + | |
| - | mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | mso-fareast-font-family: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | @list l3:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l3:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l3:level4 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l3:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l3:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l3:level7 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l3:level8 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family:" | + | |
| - | @list l3:level9 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-text: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | font-family: | + | |
| - | @list l4 | + | |
| - | {mso-list-id: | + | |
| - | mso-list-type: | + | |
| - | mso-list-template-ids: | + | |
| - | @list l4:level1 | + | |
| - | {mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level2 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level3 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level4 | + | |
| - | {mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level5 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level6 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level7 | + | |
| - | {mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level8 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | @list l4:level9 | + | |
| - | {mso-level-number-format: | + | |
| - | mso-level-tab-stop: | + | |
| - | mso-level-number-position: | + | |
| - | margin-left: | + | |
| - | text-indent: | + | |
| - | ol | + | |
| - | {margin-bottom: | + | |
| - | ul | + | |
| - | {margin-bottom: | + | |
| - | --> | + | |
| - | </ | + | |
| - | <!--[if gte mso 10]> | + | |
| - | < | + | |
| - | /* Style Definitions */ | + | |
| - | | + | |
| - | {mso-style-name:" | + | |
| - | mso-tstyle-rowband-size: | + | |
| - | mso-tstyle-colband-size: | + | |
| - | mso-style-noshow: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-parent:""; | + | |
| - | mso-padding-alt: | + | |
| - | mso-para-margin-top: | + | |
| - | mso-para-margin-right: | + | |
| - | mso-para-margin-bottom: | + | |
| - | mso-para-margin-left: | + | |
| - | line-height: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | table.MsoTableGrid | + | |
| - | {mso-style-name: | + | |
| - | mso-tstyle-rowband-size: | + | |
| - | mso-tstyle-colband-size: | + | |
| - | mso-style-priority: | + | |
| - | mso-style-unhide: | + | |
| - | border: | + | |
| - | mso-border-alt: | + | |
| - | mso-padding-alt: | + | |
| - | mso-border-insideh: | + | |
| - | mso-border-insidev: | + | |
| - | mso-para-margin: | + | |
| - | mso-para-margin-bottom: | + | |
| - | mso-pagination: | + | |
| - | font-size: | + | |
| - | font-family:" | + | |
| - | mso-ascii-font-family: | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-hansi-font-family: | + | |
| - | mso-hansi-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | mso-bidi-theme-font: | + | |
| - | mso-fareast-language: | + | |
| - | </ | + | |
| - | < | + | |
| - | < | + | |
| - | </ | + | |
| - | < | + | |
| - | <o:idmap v: | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <body lang=DE style=' | + | |
| - | + | ||
| - | <div class=WordSection1> | + | |
| - | + | ||
| - | <h1 style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | class=MTEquationSection>< | + | |
| - | lang=EN-GB style=' | + | |
| - | SEQ MTEqn \r \h \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | in Agriculture – Generating more economic sophisticated solutions< | + | |
| - | style=' | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | color:# | + | |
| - | mso-fareast-language: | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | guide as training material< | + | |
| - | name=" | + | |
| - | style=' | + | |
| - | class=MsoFootnoteReference>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | mso-fareast-theme-font: | + | |
| - | mso-bidi-font-family:" | + | |
| - | color:# | + | |
| - | EN-US; | + | |
| - | + | ||
| - | <p class=MsoNormal>< | + | |
| - | reading material should guide you theoretically through the derivation of | + | |
| - | parameter calibration of PMP terms for economically more sophisticated | + | |
| - | programming models. In this <span class=GramE> | + | |
| - | understand how a linear programming works and what the shortcomings are, how | + | |
| - | positive mathematical programming models are calibrated and how these different | + | |
| - | models behave if input parameters change.< | + | |
| - | + | ||
| - | <p class=MsoNormal>< | + | |
| - | there is a hands on excel (Session_B5_Beginners_Advanced_PMP_example.xlsx) and | + | |
| - | GAMS file (Session_B5_Advanced_PMP_example.gms) for the beginners and advanced, | + | |
| - | respectively.< | + | |
| - | title="">< | + | |
| - | footnote'>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-ascii-theme-font: | + | |
| - | minor-latin; | + | |
| - | mso-bidi-theme-font: | + | |
| - | EN-US; | + | |
| - | With the examples provided in the files you can train how to set up and solve a | + | |
| - | linear programming model, calibrate the positive mathematical programming | + | |
| - | models and simulate the price changes. You are free to also define other price | + | |
| - | changes once you are familiar with the price scenarios given here in the guide.< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | models is strongly related to the decision making situation of a farmer. | + | |
| - | Farmers must make decisions about the production plan. The decisions are not | + | |
| - | independent from physical or financial constraints. Traditionally, | + | |
| - | relied on intuition, experience or their neighbour’s actions. Using formal | + | |
| - | methods like mathematical programming models can enhance the farmers profits, | + | |
| - | at least when the production program becomes more complex. Those mathematical | + | |
| - | programming models predict quite accurately the behaviour of a representative | + | |
| - | farmer. This predictive “power” makes those representative farm models useful | + | |
| - | for policy analysis (Hazell & Norton, 1986).< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | linear programming model < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | method to find the profit maximizing combination of production activities which | + | |
| - | is feasible subject to a set of farm constraints. <span style=' | + | |
| - | 1'> | + | |
| - | + | ||
| - | <p class=MsoListParagraphCxSpFirst style=' | + | |
| - | auto; | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | |
| - | </ | + | |
| - | alternative production activities, their unit of measurement, | + | |
| - | requirements and any production constraints< | + | |
| - | + | ||
| - | <p class=MsoListParagraphCxSpMiddle style=' | + | |
| - | auto; | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | |
| - | </ | + | |
| - | fixed resource constraints< | + | |
| - | + | ||
| - | <p class=MsoListParagraphCxSpLast style=' | + | |
| - | text-align: | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-hansi-font-family: | + | |
| - | EN-GB'>< | + | |
| - | </ | + | |
| - | margins of the production activities< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | programming model for a farm is presented (Hazell & Norton, 1986). < | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | style=' | + | |
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| - | style=' | + | |
| - | style=' | + | |
| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
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| - | lang=EN-GB>< | + | |
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| - | style=' | + | |
| - | | + | |
| - | | + | |
| - | < | + | |
| - | < | + | |
| - | <v:f eqn=" | + | |
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| - | <v:f eqn=" | + | |
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| - | style=' | + | |
| - | style=' | + | |
| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
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| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
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| - | <p class=MsoListParagraphCxSpFirst style=' | + | |
| - | auto; | + | |
| - | lang=EN-GB style=' | + | |
| - | mso-hansi-font-family: | + | |
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| - | associated with the resource constraints< | + | |
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| - | production activity levels that maximize the total gross margin (<span | + | |
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| - | activity levels. The dual variables of the resource constraints (<span | + | |
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| - | values | + | |
| - | enhance the resource constraints. For instance, the shadow price of land is the | + | |
| - | maximum value of one additional unit of land to increase the most profitable | + | |
| - | production activity.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | few assumptions are made. At first, | + | |
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| - | MERGEFORMAT <span style=' | + | |
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| - | lang=EN-GB style=' | + | |
| - | It is important to have at least one nonzero constraint </ | + | |
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| - | number | + | |
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| - | can be find. The model coefficients – gross <span class=GramE> | + | |
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| - | known and constant. This also leads to the fact, that the increase of total | + | |
| - | expected gross margin and the resource requirements per unit are proportional | + | |
| - | to the used production activity level and hence, independent of the activity | + | |
| - | level used. Further it is assumed, that the resources can be used and the | + | |
| - | activities produced in quantities are fractional units. The units of the | + | |
| - | resources or activities are identical. No interaction effects between the | + | |
| - | production activities are allowed, which means, that the total product is the | + | |
| - | sum of their individual products. < | + | |
| - | + | ||
| - | <h3 style=' | + | |
| - | small example< | + | |
| - | + | ||
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| - | programming model to become familiar with mathematical programming models.< | + | |
| - | + | ||
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| - | file sheet “Simple LP”, GAMS file model “LP”)< | + | |
| - | + | ||
| - | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 | + | |
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| - | <td width=278 nowrap colspan=4 valign=top style=' | + | |
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| - | solid windowtext .5pt; | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
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| - | <td width=59 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | has to set the level of four production activities that produce four | + | |
| - | commodities. The objective function is to maximize the expected total gross | + | |
| - | margin. But at the same time the resource constraints must hold. In particular, | + | |
| - | at maximum 200 ha of land are available for each production activity and 10,000 | + | |
| - | hours of labour. Each production activity has the same requirement to the land. | + | |
| - | This means, one ha of land produces one unit of the commodity. The production | + | |
| - | activities need different amounts of labour. For example, production activity 4 | + | |
| - | needs 87 hours of labour to produce one unit of commodity four. This activity | + | |
| - | has also the greatest expected gross margin of 516 per unit. The combination of | + | |
| - | the production activities that maximizes the total gross margin and that does | + | |
| - | not violate the constraints has to be find.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | solver in Excel. The expected total gross margin <span style=' | + | |
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| - | solver of Excel gives the solution of <span style=' | + | |
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| - | resources of land and labour are totally exhausted. The farmer is advised to | + | |
| - | only use production activity two and four to maximize his profits. The shadow | + | |
| - | price of land is 391.5 and labour is 1.43. For instance, the representative | + | |
| - | farmer would pay 391.5 for one additional unit of land to enhance his | + | |
| - | production level for one of his preferred production activities.< | + | |
| - | + | ||
| - | <h3 style=' | + | |
| - | of the example< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | implementation of the linear programming model to set up a profit maximizing | + | |
| - | farm production plan. The representative farmer has the knowledge | + | |
| - | expected gross margins and resource requirements of each production activity | + | |
| - | and with that, the linear programming model is a useful tool to calculate the | + | |
| - | profit maximizing production plan.<a style=' | + | |
| - | name=" | + | |
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| - | class=MsoFootnoteReference>< | + | |
| - | 115%; | + | |
| - | mso-fareast-font-family: | + | |
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| - | mso-ansi-language: | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | activities are part of the production problem. But in reality we observe that | + | |
| - | farmers also use production activities that seem to be less profitable. The | + | |
| - | linear programming model obviously does not consider real farmer’s behaviour | + | |
| - | and produces overspecialisation. There can be several reasons why farmers use | + | |
| - | less profitable production activities. One the one hand there are governmental | + | |
| - | rules or production activity rotation requirements that force the farmer to set | + | |
| - | up a less profitable production plan. This could be handled by additional | + | |
| - | constraints. Further reasons for this behaviour can be the risk aversion of the | + | |
| - | farmer or some costs that the farmer faces for some production activities that | + | |
| - | cannot be observed and with that not be implemented with additional | + | |
| - | constraints. Additionally, | + | |
| - | programming model will increase the problem of overspecialisation.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | costs for the farmer should be the point we want to investigate in the | + | |
| - | following. The linear programming model is extended and the solution of the | + | |
| - | optimization programme should be more realistic when compared to real world | + | |
| - | behaviour.< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | mathematical programming model < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | overspecialisation and to reflect more realistic behaviour of farmers, positive | + | |
| - | mathematical programming is a methodology that calibrates programming models to | + | |
| - | observed quantities to specify appropriate non-linear objective functions | + | |
| - | (Heckelei, 2002).<a style=' | + | |
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| - | footnote'>< | + | |
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| - | EN-US; | + | |
| - | These objective functions are modifications of the traditional objective | + | |
| - | function used in linear programming models and have terms that can be | + | |
| - | interpreted to capture the unobserved behaviour of the farmer and hence, should | + | |
| - | lead to more realistic optimization solutions.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | programming approach can be separated into three steps (Howitt, 1995). At | + | |
| - | first, the optimization model is forced to reproduce observed activity levels. | + | |
| - | Second, the dual values of the calibration constraints are used for the | + | |
| - | modification of the objective function. Third, the new model is employed for | + | |
| - | simulations.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | model builds on the basis of the linear programming model and is extended only | + | |
| - | by additional constraints. These are the calibration constraints:< | + | |
| - | + | ||
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| - | production activity levels< | + | |
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| - | associated with the calibration constraints< | + | |
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| - | programming model. In the first step, the optimal solution of this positive | + | |
| - | mathematical programme <span class=GramE> | + | |
| - | the observed production activity levels (<span style=' | + | |
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| - | distinguished into preferable and marginal activities. Preferable production | + | |
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| - | of the calibration constraints are zero for the marginal activities (<span | + | |
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| - | cost for preferable activities (<span style=' | + | |
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| - | the objective function entries and the coefficients of the marginal activities | + | |
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| - | resources only depend on the marginal activities, interaction between the | + | |
| - | production activities are not covered. With the dual values of the calibration | + | |
| - | constraints, | + | |
| - | model is captured.< | + | |
| - | + | ||
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| - | mathematical programming approach the dual values of the preferable activities | + | |
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| - | function. The extension of the former objective function of the linear | + | |
| - | programming model implies a variable cost function which leads to the omission | + | |
| - | of the calibration constraints of the mathematical programming model in the | + | |
| - | first step.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
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| - | parameters of a variable cost function such that the economic rule marginal | + | |
| - | revenue equals marginal cost holds at observed activity levels. Most often, a | + | |
| - | quadratic cost function is used.< | + | |
| - | + | ||
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| - | function can be specified like:< | + | |
| - | + | ||
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| - | solution of the linear programming model.< | + | |
| - | + | ||
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| - | function that satisfy the conditions to calibrate to observed activity levels | + | |
| - | when solving the positive mathematical programming model are infinite. But the | + | |
| - | different combinations of parameters lead to different response behaviour to | + | |
| - | changing economic conditions (see Heckelei (2002) for technical proof).< | + | |
| - | + | ||
| - | <h3 style=' | + | |
| - | the parameters of the new objective function< | + | |
| - | + | ||
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| - | parameters of the new objective function.< | + | |
| - | href="# | + | |
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| - | class=MsoFootnoteReference>< | + | |
| - | 115%; | + | |
| - | mso-fareast-font-family: | + | |
| - | minor-latin; | + | |
| - | mso-ansi-language: | + | |
| - | Some of them are presented in the following (Heckelei, 2002). Here we present | + | |
| - | only a few. In the CAPRI training course we will elaborate additional | + | |
| - | specification rules.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | very simply ((e.g. Howitt and Mean, 1983; <span class=SpellE> | + | |
| - | Paris, 1995)). Just setting <span style=' | + | |
| - | mso-text-raise: | + | |
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| - | DrawAspect=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | off-diagonal elements of <span style=' | + | |
| - | -6.0pt'>< | + | |
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| - | </ | + | |
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| - | elements as:< | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | style=' | + | |
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| - | style=' | + | |
| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
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| - | lang=EN-GB>< | + | |
| - | lang=EN-GB>< | + | |
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| - | | + | |
| - | < | + | |
| - | o: | + | |
| - | </ | + | |
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| - | DrawAspect=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | top: | + | |
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| - | </ | + | |
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| - | DrawAspect=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | the marginal activities are zero. The objective function of that specification | + | |
| - | rule would be:< | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
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| - | style=' | + | |
| - | style=' | + | |
| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB>< | + | |
| - | lang=EN-GB>< | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | | + | |
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| - | o: | + | |
| - | </ | + | |
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| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | function with another rule. He set <span style=' | + | |
| - | mso-text-raise: | + | |
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| - | </ | + | |
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| - | </ | + | |
| - | </ | + | |
| - | off-diagonal elements <span class=GramE> | + | |
| - | top: | + | |
| - | | + | |
| - | < | + | |
| - | o: | + | |
| - | </ | + | |
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| - | DrawAspect=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB>< | + | |
| - | lang=EN-GB>< | + | |
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| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
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| - | </ | + | |
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| - | DrawAspect=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | the marginal activities are not zero as before and the new objective function | + | |
| - | would be:< | + | |
| - | + | ||
| - | <p class=MTDisplayEquation style=' | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | SEQ MTSec \c \* Arabic \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB>< | + | |
| - | lang=EN-GB>< | + | |
| - | lang=EN-GB>< | + | |
| - | style=' | + | |
| - | | + | |
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| - | </ | + | |
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| - | DrawAspect=" | + | |
| - | </ | + | |
| - | </ | + | |
| - | + | ||
| - | <h3 style=' | + | |
| - | the positive mathematical programming approach < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | new objective function in the positive mathematical programming model is now | + | |
| - | applied and the results are presented regarding the parameters of the cost | + | |
| - | functions.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | style=' | + | |
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| - | yes'> | + | |
| - | < | + | |
| - | </ | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | a positive mathematical programming model. It is quite the same as in the | + | |
| - | linear programming model of </ | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | yes'> | + | |
| - | < | + | |
| - | </ | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | it is convenient to split the gross margin into price and cost per unit of a | + | |
| - | level of production activity. Second – and this is important for the positive | + | |
| - | mathematical programming approach – the addition of 4 calibration constraints. | + | |
| - | The model is forced to solve this optimization problem to have the observed | + | |
| - | production activity levels (x1=55; x2=30; x3=85 and x4=30) recalibrated. <span | + | |
| - | style=' | + | |
| - | + | ||
| - | <p class=MsoCaption style=' | + | |
| - | name=" | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | EN-US'>< | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-US style=' | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | lang=EN-US style=' | + | |
| - | mathematical< | + | |
| - | “PMP reveal dual values”, GAMS file model “Howitt_1”)</ | + | |
| - | + | ||
| - | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 | + | |
| - | | + | |
| - | | + | |
| - | < | + | |
| - | <td width=164 nowrap valign=top style=' | + | |
| - | mso-border-alt: | + | |
| - | <td width=278 nowrap colspan=4 valign=top style=' | + | |
| - | border-left: | + | |
| - | solid windowtext .5pt; | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | style=' | + | |
| - | </ | + | |
| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | solid windowtext .5pt; | + | |
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| - | solid windowtext .5pt; | + | |
| - | </ | + | |
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| - | <td width=164 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | line-height: | + | |
| - | style=' | + | |
| - | </ | + | |
| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | style=' | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | mso-border-alt: | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | margin-left: | + | |
| - | style=' | + | |
| - | mso-ansi-language: | + | |
| - | </ | + | |
| - | <td width=76 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <td width=67 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-ascii-font-family: | + | |
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| - | </ | + | |
| - | <td width=67 nowrap valign=bottom style=' | + | |
| - | border-left: | + | |
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| - | </ | + | |
| - | <td width=59 nowrap valign=bottom style=' | + | |
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| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | text-align: | + | |
| - | mso-ascii-font-family: | + | |
| - | Calibri'> | + | |
| - | </ | + | |
| - | <td width=75 nowrap valign=bottom style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | text-align: | + | |
| - | mso-ascii-font-family: | + | |
| - | Calibri'> | + | |
| - | </ | + | |
| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal style=' | + | |
| - | justify; | + | |
| - | mso-ansi-language: | + | |
| - | </ | + | |
| - | <td width=134 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
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| - | margin-left: | + | |
| - | lang=EN-GB style=' | + | |
| - | </ | + | |
| - | </ | + | |
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| - | <td width=164 nowrap valign=top style=' | + | |
| - | border-top: | + | |
| - | padding:0cm 5.4pt 0cm 5.4pt; | + | |
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| - | margin-left: | + | |
| - | style=' | + | |
| - | mso-ansi-language: | + | |
| - | </ | + | |
| - | <td width=76 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | mso-border-alt: | + | |
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| - | EN-GB'> | + | |
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| - | border-left: | + | |
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| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=75 nowrap valign=top style=' | + | |
| - | border-left: | + | |
| - | mso-border-top-alt: | + | |
| - | mso-border-alt: | + | |
| - | <p class=MsoNormal align=center style=' | + | |
| - | margin-bottom: | + | |
| - | line-height: | + | |
| - | EN-GB'> | + | |
| - | </ | + | |
| - | <td width=32 nowrap valign=top style=' | + | |
| - | border-left: | + | |
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| - | margin-left: | + | |
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| - | </ | + | |
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| - | mso-border-top-alt: | + | |
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| - | lang=EN-GB style=' | + | |
| - | </ | + | |
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| - | border-top: | + | |
| - | padding:0cm 5.4pt 0cm 5.4pt; | + | |
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| - | class=SpellE>< | + | |
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| - | <td width=75 nowrap valign=top style=' | + | |
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| - | <td width=134 nowrap valign=top style=' | + | |
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| - | given the constraints. The solution of this optimization problem reveals that | + | |
| - | only the resource of land is totally exhausted. One should remember that in the | + | |
| - | linear programming model solution both resources are totally exhausted. In this | + | |
| - | case, the marginal activity is x1 and the preferred activities are x2, x3 and | + | |
| - | x4. Therefore, we only have dual values for x2, x3 and x4 and with that; we | + | |
| - | have only three out of four diagonal elements larger than zero to specify our | + | |
| - | new objective function. </ | + | |
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| - | 115%; | + | |
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| - | model “Howitt_11”)< | + | |
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| - | simulation behaviour regarding price changes. Therefore, we change the prices | + | |
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| - | of the commodities of the production activities. Only p1 and p3 are increasing, | + | |
| - | p2 and p4 are remaining constant. Price p1 increases with 40 units and price p3 | + | |
| - | with 60 units with each scenario step.< | + | |
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| - | solved again with the different sets of prices. For the linear programming | + | |
| - | model, the most profitable levels of production activities for each price | + | |
| - | scenario depict </ | + | |
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| - | the first two price scenarios no adaption of the production programme of the | + | |
| - | representative farmer is profitable. For the other two price scenarios the | + | |
| - | optimal production were changed to x3=123.3 and x4= 76.7 for scenario 3 and | + | |
| - | x3=200 for scenario 4.< | + | |
| - | + | ||
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| - | production activities of the linear programming model activities (Excel file | + | |
| - | sheet “Simple LP”, GAMS file model “LP”)< | + | |
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| - | of production activities of the model with the objective <span class=GramE> | + | |
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| - | MERGEFORMAT <span style=' | + | |
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| - | lang=EN-GB style=' | + | |
| - | the production activities x1, x2, and x4 are declining whereas the level of | + | |
| - | production x4 is increasing. Although the price of commodity of production | + | |
| - | activity x1 is increasing, the optimal level of it is decreasing. This is due | + | |
| - | to the fact that the gross margin of x3 is increasing even higher than for x1 in | + | |
| - | every new price scenario.< | + | |
| - | name=" | + | |
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| - | 115%; | + | |
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| - | model “Howitt_11”)< | + | |
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| - | of production activities of the model with the objective <span class=GramE> | + | |
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| - | the level of the production activity x3 is increasing. This is also due to the | + | |
| - | fact that the gross margin of x3 is increasing even higher than for x1 and the | + | |
| - | other production activities with every new price scenario.< | + | |
| - | + | ||
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| - | + | ||
| - | <h3 style=' | + | |
| - | of simulation< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | differences between the linear and the positive mathematical programming | + | |
| - | approaches. The reaction of the linear programming model to price changes shows | + | |
| - | erratic adaptions of the production programme induced by price changes. It | + | |
| - | takes a while until the production programme changes when the model is optimized. | + | |
| - | These changes are also very strong. This means that between the second and | + | |
| - | third price scenario the production programme differs completely and the fourth | + | |
| - | price scenario induce a production plan with only one production activity. This | + | |
| - | behaviour seems very unlikely in reality.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | GOTOBUTTON ZEqnNum923545< | + | |
| - | style=' | + | |
| - | ZEqnNum923545 \* Charformat \! \* MERGEFORMAT <span style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | programming approach shows a smoother reaction to price changes compared to the | + | |
| - | linear programming model. But it can be seen that the adaption of the | + | |
| - | production programme is still relatively erratic. But the reaction to price | + | |
| - | changes seems to be much more likely than in the linear programming model.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | GOTOBUTTON ZEqnNum279523< | + | |
| - | style=' | + | |
| - | style=' | + | |
| - | <span style=' | + | |
| - | field-end'></ | + | |
| - | style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | sophisticated reaction to price changes compared to the other simulated models. | + | |
| - | The adaption of the production plan induced by price changes is very smooth and | + | |
| - | is much more realistic. There is no overspecialisation and overreaction like in | + | |
| - | the other two models.< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | linear farm production model and the extension based on the positive | + | |
| - | mathematical programming approach to be able to produce more realistic production | + | |
| - | plans when it comes to profit maximization. The positive mathematical | + | |
| - | programming approach calibrates a programming model to observed production | + | |
| - | behaviour. This is achieved with calibration constraints and the dual values of | + | |
| - | the calibration constraints are used to specify a new objective function that | + | |
| - | reflects observed farm behaviour that cannot be captured with additional | + | |
| - | constraints. These new objective functions capture a lot of possible <span | + | |
| - | class=SpellE> | + | |
| - | technology, risk behaviour or other non-linear constraints.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | specifications of cost functions. There a many ways to specify these functions | + | |
| - | and each of them imply different behaviour to changing economic circumstances. | + | |
| - | Additionally to the specifications shown in this paper there are others as | + | |
| - | well. The average-cost-approach (Heckelei, 2002) or the use of exogenous supply | + | |
| - | elasticities (Heckelei, 2002; empirically applied by Helming et al., 2001) are | + | |
| - | some of them, which will elaborated in the CAPRI training course in Seville. | + | |
| - | You can also have a closer look at them in the Excel file sheet “PMP2” and | + | |
| - | “PMP4” as well as in the GAMS file models “Howitt_12” and “Elasticities1”, | + | |
| - | respectively.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | style=' | + | |
| - | objective functions are not unproblematic. As these procedures capture the | + | |
| - | observed behaviour, a change in economic incentives of the farmer(s) over time inducing | + | |
| - | other behaviour is not observed and must come from other sources. Other | + | |
| - | shortcomings of these approaches of positive mathematical programming models can | + | |
| - | be found in the literature (see Heckelei (2002) for an overview).< | + | |
| - | + | ||
| - | <h2 style=' | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | class=SpellE>< | + | |
| - | lang=EN-GB style=' | + | |
| - | mathematical programming model for regional analysis of agricultural policies. | + | |
| - | In: <span class=SpellE> | + | |
| - | Agricultural Economics and Policies, EAAE, Proceedings of the 40th Seminar, | + | |
| - | 26.-28. <span class=SpellE> | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | (1986): Mathematical Programming for Economic Analysis in Agriculture, | + | |
| - | Macmillan Publishing Company.< | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | estimation of programming models for agricultural supply analysis. <span | + | |
| - | class=SpellE> | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | class=SpellE> | + | |
| - | of Environmental Policy Scenarios in Flemish Agriculture. In: Heckelei, T., | + | |
| - | Witzke, H.P. and <span class=SpellE> | + | |
| - | Sector Modelling and Policy Information Systems. Proceedings of the 65 <span | + | |
| - | class=SpellE>< | + | |
| - | at Bonn University, <span class=SpellE> | + | |
| - | Kiel, pp. 237-245. < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Mathematical Programming< | + | |
| - | Journal of Agricultural Economics</ | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Approach to Microeconomic Programming Models. Working Paper (6). Department of | + | |
| - | Agricultural Economics, University of California, Davis. < | + | |
| - | + | ||
| - | <p class=MsoNormal style=' | + | |
| - | lang=EN-GB style=' | + | |
| - | Parametric Programming and Comparative Statics. Chapter | + | |
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| - | of California, Davis. < | + | |
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| - | (2001): Analyse der Produktions- und Einkommenseffekte von | + | |
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| - | GAMS file are already completely working. But you must be familiar how to user | + | |
| - | the solver in excel and how to run a GAMS file. Be careful how to set all the | + | |
| - | constraints to get the desired behaviour of the models!< | + | |
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| - | model is an optimization model, in which an objective function is maximized or | + | |
| - | minimized subject to some constraints. In our case we have a maximization | + | |
| - | problem which is also called the primal model. The total gross margin is | + | |
| - | maximized while land and labour use are constrained. This problem can be | + | |
| - | transformed into a minimization problem (dual model), in which land and labour | + | |
| - | use has to be minimized while the total gross margins of each activity are | + | |
| - | constrained to have a certain minimum. The maximum value of the objective | + | |
| - | function of the primal model is always the same like the value of the objective | + | |
| - | function of the dual model. See Hazell & Norton (1986) for a more detailed | + | |
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| - | used for optimization and an optimal solution is found, you have to choose the | + | |
| - | “sensitivity analysis report” to extract the dual values of the calibration | + | |
| - | constraints. In the GAMS file you can see that after a model is solved, the | + | |
| - | dual values are captured as follows: <span class=GramE> | + | |
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| - | even higher compared to the other production activities.< | + | |
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| + | The rest of the document largely follows the workflow of the model: the different steps of building up the national, regional and global data base provide the foundations on which the system rests (Chapter 3). Subsequently the procedure needed to establish a baseline (Chapter 4) is discussed. Chapter 5 deals with the scenario impact analysis, giving descriptions for the regional supply models as well as for the global market model and their interactions in scenario runs. Chapter 6 covers some elements of post model analysis, whereas Chapter 7 covers options for spatial downscaling of the NUTS2 results. At the very end (Chapter 8), some developer tools for stability analysis are described. | ||
start.txt · Last modified: 2022/11/07 10:23 by 127.0.0.1